Hybrid pupil filter design using Bessel series

We propose a simple method of designing pupil filters for transverse super-resolution. For this end we represent the amplitude Point Spread Function (PSF) as a series expansion, constructed from the Fourier transform of a basis of Bessel functions. With this representation we optimize the intensity PSF according to certain desired characteristics, such as a smaller disk diameter than the corresponding, clear aperture, Airy disk. It is proved that by using few basis functions, it is possible to design pupils with similar or better PSF characteristics than previously reported.